Efficiently simulating many-body localisation

Dr Zlatko Papic's paper has been published in Physical Review Letters.

The amount of quantum entanglement in a many-body wave function determines whether it can be efficiently compressed and encoded by a small number of classical parameters. Ground states of many-body systems are known to have low entanglement, and can be efficiently simulated by the so-called "matrix product states" -- the property which underlies the success of the density-matrix renormalisation group.

In this Letter, we characterise the entanglement of highly excited states in many-body localised (MBL) systems by studying its "entanglement spectrum". MBL phases have been a subject of much recent interest as phases of matter that break ergodicity and thus avoid thermalisation. We argue that the entanglement structure of MBL states, while different from ground states, still allows for compact parametrisation by matrix product states. We develop an efficient algorithm to obtain highly excited states of large MBL systems. This work opens a door for studying a broad class of disordered quantum systems, inaccessible by other techniques. We expect that the new algorithm will also give a much-needed insight into the nature of the transition between MBL and ergodic (thermal) phases.